# Browsing by Author "Liu, Jian-Guo"

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Item Open Access An Exploratory Radiomics Approach to Quantifying Pulmonary Function in CT Images(Scientific Reports, 2019-12) Lafata, Kyle J; Zhou, Zhennan; Liu, Jian-Guo; Hong, Julian; Kelsey, Chris R; Yin, Fang-FangItem Open Access Association of pre-treatment radiomic features with lung cancer recurrence following stereotactic body radiation therapy.(Physics in medicine and biology, 2019-01-08) Lafata, Kyle J; Hong, Julian C; Geng, Ruiqi; Ackerson, Bradley G; Liu, Jian-Guo; Zhou, Zhennan; Torok, Jordan; Kelsey, Chris R; Yin, Fang-FangThe purpose of this work was to investigate the potential relationship between radiomic features extracted from pre-treatment x-ray CT images and clinical outcomes following stereotactic body radiation therapy (SBRT) for non-small-cell lung cancer (NSCLC). Seventy patients who received SBRT for stage-1 NSCLC were retrospectively identified. The tumor was contoured on pre-treatment free-breathing CT images, from which 43 quantitative radiomic features were extracted to collectively capture tumor morphology, intensity, fine-texture, and coarse-texture. Treatment failure was defined based on cancer recurrence, local cancer recurrence, and non-local cancer recurrence following SBRT. The univariate association between each radiomic feature and each clinical endpoint was analyzed using Welch's t-test, and p-values were corrected for multiple hypothesis testing. Multivariate associations were based on regularized logistic regression with a singular value decomposition to reduce the dimensionality of the radiomics data. Two features demonstrated a statistically significant association with local failure: Homogeneity2 (p = 0.022) and Long-Run-High-Gray-Level-Emphasis (p = 0.048). These results indicate that relatively dense tumors with a homogenous coarse texture might be linked to higher rates of local recurrence. Multivariable logistic regression models produced maximum [Formula: see text] values of [Formula: see text], and [Formula: see text], for the recurrence, local recurrence, and non-local recurrence endpoints, respectively. The CT-based radiomic features used in this study may be more associated with local failure than non-local failure following SBRT for stage I NSCLC. This finding is supported by both univariate and multivariate analyses.Item Open Access Emergence of step flow from an atomistic scheme of epitaxial growth in 1+1 dimensions.(Phys Rev E Stat Nonlin Soft Matter Phys, 2015-03) Lu, Jianfeng; Liu, Jian-Guo; Margetis, DionisiosThe Burton-Cabrera-Frank (BCF) model for the flow of line defects (steps) on crystal surfaces has offered useful insights into nanostructure evolution. This model has rested on phenomenological grounds. Our goal is to show via scaling arguments the emergence of the BCF theory for noninteracting steps from a stochastic atomistic scheme of a kinetic restricted solid-on-solid model in one spatial dimension. Our main assumptions are: adsorbed atoms (adatoms) form a dilute system, and elastic effects of the crystal lattice are absent. The step edge is treated as a front that propagates via probabilistic rules for atom attachment and detachment at the step. We formally derive a quasistatic step flow description by averaging out the stochastic scheme when terrace diffusion, adatom desorption, and deposition from above are present.Item Open Access Pseudo-differential Operators, Online PCA Flows and the Linear Response Theory(2023) Liu, ZibuThree problems will be considered in this dissertation.

First, the well-posedness and numerical simulation of PDEs involving pseudo-differential operators are considered.

One example is the water wave equation. Lack of rigorous analysis of its time discretization inhibits the design of more efficient algorithms. First, a model simplified from the water wave equation of infinite depth is considered. This model preserves two main properties of the water wave equation: non-locality and hyperbolicity. Systematic stability studies of the fully discrete approximation of such systems is also complemented. As a result, an optimal time discretization strategy is provided in the form of a modified CFL condition, i.e. $\Delta t=O(\sqrt{\Delta x})$. Meanwhile, the energy stable property is established for certain explicit Runge-Kutta methods.

Another example is the vectorial Peierls-Nabarro model. First, a non-local scalar Ginzburg-Landau equation with an anisotropic positive singular kernel is derived from the original model. We first prove that minimizers of the PN energy for this reduced scalar problem exist. We also prove that these minimizers are smooth 1D profiles. Then a De Giorgi-type conjecture of single-variable symmetry for both minimizers and layer solutions is established. The proof of this De Giorgi-type conjecture relies on a delicate spectral analysis which is especially powerful for nonlocal pseudo-differential operators with strong maximal principle.

The second problem is the Online principal component analysis (PCA). It has been an efficient tool in practice to reduce dimension. However, convergence properties of the corresponding ODE (the deterministic flow) are still not fully unknown. A new technique is developed to determine stable manifolds of the ODE. This technique analyzes the rank of the initial datum. Using this technique, we derived the explicit expression of the stable manifolds. As a consequence, exponential convergence to stable equilibrium points was proved. The success of this new technique should be attributed to the semi-decoupling property of the SGA method: iteration of previous components does not depend on that of later ones.

The convergence property of the discrete algorithm is also considered. The algorithm is viewed as a stochastic process on the parameter space and semi-group. First, the discrete algorithm can be viewed as a semigroup: $S^k\varphi=\E[\varphi(\mb W(k))]$. Second, stochastic differential equations (SDEs) are constructed on the Stiefel manifold, i.e. the diffusion approximation, to approximate the semigroup. By weak convergence, the algorithm is 'close to' the SDEs. Finally, reversibility of the SDEs to prove long time convergence.

The third problem is the rigorous verification of the linear response theory (LRT). This theory considers the response of a system at equilibrium to external perturbations. It assumes that eh response is a linear functional of the perturbation. In particular, Langevin dynamics is considered. Equivalent conditions of reversibility of Langevin dynamics are proposed. Then, utilizing the ergodicity of Fokker-Planck equations, the response functional is rigorously verified for both over-damped and under-damped Langevin dynamics. As a corollary, the Green-Kubo relation is also verified.